The use of maximum entropy and likelihood ranking to determine the crystal structure of 4-(4′-(N,N-dimethyl)aminobenzylidene)-pyrazolidine-3,5-dione at 1.4 Å resolution from electron diffraction and high-resolution electron microscopy image data

Electron crystallography of organic materials

The application of electron crystallography to the study of organic materials is reviewed, mainly in context of the author's own experience. Direct methods for crystallographic phase determination have been shown to be very effective for ab initio structure analyses with electron diffraction intensities, permitting the elucidation of previously uncharacterized crystal structures. Fruitful applications areas have included chain-folded linear polymers, pigments, polydisperse linear chain arrays and, surprisingly, the subgroup assembly of certain proteins.

A practical method to detect and correct for lens distortion in the TEM

A practical, offline method for experimental detection and correction for projector lens distortion in the transmission electron microscope (TEM) operating in high-resolution (HR) and selected area electron diffraction (SAED) modes is described. Typical TEM works show that, in the simplest case, the distortion transforms on the recording device, which would be a circle into an ellipse. The first goal of the procedure described here is to determine the elongation and orientation of the ellipse. The second goal is to correct for the distortion using an ordinary graphic program. The same experimental data set may also be used to determine the actual microscope magnification and the rotation between SAED patterns and HR images. The procedure may be helpful in several quantitative applications of electron diffraction and HR imaging, for instance while performing accurate lattice parameter determination, or while determining possible metrical deviations (cell edges and angles) from a given symmetry.

Solving modulated structures by X-ray and electron crystallography

X-ray diffraction can be used for accurately determining not only classical, ordinary structures, but also modulated ones. For structures with weak modulations, the modulation induced satellite reflections are often hard to be observed by X-ray diffraction, but they appear clearly in electron diffraction. In these cases, X-ray diffraction will give only average structures whereas electron diffraction will yield information about the modulations. Sr(1.4)Ta(0.6)O(2.9) is a complex modulated compound with weak modulation and small modulated domains. Here we demonstrate the power of combining X-ray and electron crystallography for studying modulated structures on powders. The modulations of Sr(1.4)Ta(0.6)O(2.9) were determined from electron diffraction (SAED) and high resolution electron microscopy (HREM) images. With specially developed image processing techniques, the weak modulations were enhanced, facilitating the interpretation of HREM images in terms of atomic structure.

Comparison of electron diffraction data from non-linear optically active organic DMABC crystals obtained at 100 and 300 kV

During the recent past, we have synthesized a new class of molecules with intramolecular two-dimensional charge transfer upon excitation. The present report presents such a molecule, 2,6-bis(4-dimethylamino-benzylidene)-cyclohexanone (DMABC), with an unusually high value of the second-order non-linear optical (NLO) coefficients. In order to optimize the macroscopic NLO properties of the compounds, it is necessary to relate their first hyperpolarizability tensors at a molecular level to those at a crystal bulk level. This requires a complete structure determination and refinement. However, the growth of sufficiently large single crystals, which are needed for structural analysis and refinement by X-ray methods, is a time consuming and sometimes impossible task. We have performed a complete structural analysis by electron diffraction combined with simulation methods and with maximum entropy and log likelihood statistics. In order to improve the quantitative analysis, a 300 kV data set using an on-line CCD camera was added and the best attainable R-values were compared with those from 100 kV data using film emulsions. Details regarding the maximum attainable resolution for both data sets are discussed as well as the problems which arise from the limited dynamic range in photographic emulsions as compared to a 14 bit CCD camera. Once the crystal structure was known, quantum-chemical methods were used to calculate non-linear optical susceptibility tensor components and these were related to the macroscopic coefficients of the crystalline quadratic non-linearity tensor. In the present work, both ab initio and semi-empirical quantum-chemical calculations were employed.

On the phase problem in electron microscopy: the relationship between structure factors, exit waves, and HREM images

In electron microscopy, the word phase is used for different physical phenomena, including crystallographic structure-factor phases and the electron wave phases. This has resulted in great confusion, as to whether the phase information is present or lost when an image is recorded. The aim of this paper is to solve this phase confusion problem by studying the relationships between structure factors, exit waves, and high-resolution electron microscopy (HREM) images. Three approaches are taken. First phases at different stages of the imaging processes are compared analytically for a crystal that can be considered a weak phase object (WPO). Then these different phases are calculated by the multi-slice method based on dynamical diffraction theory, and their numerical values are compared. Finally, the validity of the theoretical description is checked by comparison with experimental data on a real crystal, Ti(2)S. It is demonstrated that it is possible to obtain accurate structure factor-phases directly from HREM images by crystallographic image processing. The two major methods for structure determination from HREM images-exit wave reconstruction and crystallographic image processing-are compared. It is shown that the information utilised by the two methods as well as the results are essentially the same.

Maximum entropy methods in electron crystallography

The maximum entropy (ME) method of solving crystal structures in two or three dimensions from electron diffraction data is described. Applications to organic and inorganic molecules, membrane proteins and surface structures are outlined, and the power of the ME formalism to deal with incomplete and error prone data is demonstrated.